I. \(x \# y = y \# x\) \(x \# y = (x + y)(x - y) = x^2 - y^2\) \(y \# x = (y + x)(y - x) = y^2 - x^2\) 并非总是成立 II. \(x \# 0 = 0 \# x = x^2\) \(x \# 0 = (x + 0)(x - 0) = x^2\) \(0 \# x = (0 + x)(0 - x) = -x^2\) III. \(x \# (-y) = x \# y\) \(x \# (-y) = [x + (-y)][x - (-y)] = (x - y)(x + y) = x^2 - y^2\) \(x \# y = (x - y)(x + y) = x^2 - y^2\) 因此，选 C。